Quantum logics and Lindenbaum property. (English) Zbl 0634.03065
It is shown that both orthomodular quantum logics (orthomodular lattices) and partial classical logics (based on partial Boolean algebras) cannot satisfy the Lindenbaum property, which asserts that any semantically non- contradictory set of formulas admits a semantically non-contradictory extension.
Reviewer: A.Dvurečenskij
MSC:
| 03G12 | Quantum logic |
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
| 81P20 | Stochastic mechanics (including stochastic electrodynamics) |
Keywords:
partial quantum logic; orthomodular quantum logics; orthomodular lattices; partial classical logics; partial Boolean algebras; Lindenbaum propertyReferences:
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